<p>I am a freshman in High School, and I am very interested about the engineering field.</p>
<p>I haven't taken Calculus yet but my question is how is Calculus different from Algebra?</p>
<p>I was actually thinking about how I would ever be able to describe to someone what calculus exactly is. (I am senior in High School taking AP BC Calculus) Its really hard to explain because in Algebra you have to solve for a "y" but in calculus, you can solve for two or more variables. It really isn't as difficult or "complex" as it sounds. If I HAVE to describe it...then calculus would be, basically, finding the area under a curve.</p>
<p>you can solve for multiple variables using only algebra.</p>
<p>you can view calculus as an extension of mathematics beyond algebra. just as arithmetic knowledge is required to do algebra, a strong foundation in algebra is required to do calculus.</p>
<p>calculus concepts tend to be more abstract and require more in depth understanding, while algebra tends to be more mechanical in nature.</p>
<p>a couple examples of applications that you will encounter right away in introductory calculus include finding areas under non-uniform curves, finding instantaneous change in direction, or determining volume of a solid when a curve is rotated around a specific axis.</p>
<p>Calculus is the math/science of continuity and because of that, you can calculate the rate of how things change via some parameter or find the area under a continuous curve that varies with time.</p>
<p>The Limit (what allows calculus to work):
The idea is that you can break any curve (or surface) into an infinite number of subpieces and see what happens when you take the slope (rise over run) or find the area (by adding up the squares) as the size of the subpieces shrink to essentially 0. Limits can approach other numbers that are interesting (such as infinite or a number) as well. The idea is that you can get really really close to that number but never hit it. But because you are so close and you can see what the ouput is of the function, you can figure out what happens at that point you cannot evaluate at. </p>
<p>Rate of change (also called differentiation):
if y = x, then the rate of change (or slope) of the equation will always be 1.
but if y = x^2, then it turns out that rate of change depends on x and is 2x. (That makes sense, right? On the graph, as x increases, the slope of the curve increases!)</p>
<p>Area under the curve (also called integration):
From geometry, if y=x, you should be able to find the area under the curve. (1/2 length x height, right?) But what happens when the function is non-linear? For instance, what happens when y = x^2 ? Calculus breaks up the curve into an infinite little pieces that are then added together to form the area (with no error!). It turns out that the area under y = x^2 is y = (1/3)x^3. You have to evaluate this to get the actual number but I'm not sure you're ready for that yet.</p>
<p>What was stated in the prior posts pretty much sums it up about Calculus.</p>
<p>Even if you don't take Calculus in high-school, if you get as far as Analytic Geometry...then you can start off with Calculus in college.</p>